To flirt and attempt to get a girl to be attracted to you. Has no real derivation, but I sometimes think of it as tuning the girl to your station, not disimilar from a radio.
The act of 'tuning' ceases the moment you kiss the girl or a relationship is formed.
A 'tune mission' is going for a walk, mission or outing with the aim of meeting, tuning and hopefully scoring with hot chicks.